# Commutator of the matrices of the rotation group

1. May 28, 2015

### spaghetti3451

Consider the rotation group $SO(3)$.

I know that $R_{x}(\phi) R_{z}(\theta) - R_{z}(\theta) R_{x} (\phi)$ is a commutator?

But can this be called a commutator $R_{z}(\delta \theta) R_{x}(\delta \phi) R_{z}^{-1}(\delta \theta) R_{x}^{-1} (\delta \phi)$?

2. May 28, 2015

### Fredrik

Staff Emeritus
I haven't seen anyone use that term for anything other than expressions of the form AB-BA.

3. May 28, 2015

### spaghetti3451

I found it in page 31 of Ryder's 'Quantum Field Theory' - second edition.

4. May 28, 2015